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soldi70 [24.7K]
3 years ago
12

Triangle X Y Z is shown. The length of side X Y is (9 n + 12) feet and the length of side X Z is (15 n minus 6) feet. Angles X Y

Z and Y Z X are congruent. Consider isosceles ΔXYZ. What is the value of n? What is the measure of leg XY? ft What is the measure of leg XZ? ft
Mathematics
1 answer:
zmey [24]3 years ago
7 0

Answer:

n = 3

XY = 39

XZ = 39

Step-by-step explanation:

Given

XY = 9n + 12

XZ = 15n - 6

Solving (a): n

To solve for n;

We make use of

XY = XZ

Substitute values for XY and XZ

9n + 12 = 15n - 6

9n - 15n = -12 - 6

-6n = -18

Divide through by -6

n = 3

Solving (b) XY

XY = 9n + 12

Substitute 3 for n

XY = 9 * 3 + 12

XY = 27 + 12

XY = 39

Solving (c): XZ

XZ = XY

XZ = 39

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Answer:

It takes 4 minutes per block and she can walk 12.5 blocks in 45 minutes.

Step-by-step explanation:

20 / 5 = 4 minutes per block

20 + 20 + 5 = 45

5 + 5 + 2.5 = 12.5

Hope this helps, I did the test last year.

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5 0
3 years ago
Please I need help ASAP<br>pls explain your answer ​
USPshnik [31]

Answer:

47.62 cm

Step-by-step explanation:

ABCD is a rhombus. Each side measures 15 cm.

m<A = 60°.

Here are some properties of a rhombus:

Opposite angles of a rhombus are congruent.

m<C = m<A = 60°

m<ADC = m<ABC

The sum of the measures of the interior angles of a quadrilateral is 360°.

The diagonals are perpendicular bisectors of each other.

m<A + m<C + m<ADC + m<ABC = 360°

60° + 60° + 2m<ADC = 360°

2m<ADC = 240°

m<ADC = 120°

Each diagonal of a rhombus bisects a pair of congruent, opposite angles.

m<ADB + m<CDB = m<ADC

m<ADB = m<CDB

m<ADB + m<ADB = 120°

m<ADB = 60°

Triangle ABD had two angles, <A and <ADB, that measure 60°. Therefore, the third angle, <ABD also measures 60°. That makes triangle ABD an equilateral triangle.

Draw segment AT.

T is the midpoint of BD. The segment AT is the perpendicular bisector of segment BD. Triangle ATD is a 30-60-90 triangle.

Using the ratio of the lengths of the sides of a 30-60-90 triangle, we can calculate the length of AT which is the radius of circle A.

TD : AT : AD

1    : √3 :   2

AD = 15 cm

TD = AD/2

AT = √3 × TD

AT = (AD√3)/2

AT = 7.5√3 = 12.99

AQ = 12.99

perimeter = QD + PB + m(arc)PTQ + BC + CD

perimeter = (15 - 12.99) + (15 - 12.99) + 60°/360° × 2π(12.99) + 15 + 15

perimeter = 47.62

Answer: perimeter = 47.62 cm

7 0
2 years ago
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Alecsey [184]

Answer:

$44

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Original price = $80

Discount on sale = 50%

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Sales tax amount = 0.1 * $40 = $4

Total cost = discounted price + sales tax amount

Total cost = $40 + $4 = $44

5 0
3 years ago
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